More General Conditions for Stability

Abstract

Here we shall prove that the least n for which $\frac{{{\partial^n}V}}{{\partial x\begin{array}{*{20}{c}} n \\ 1 \\ \end{array} }}\left( {0,0} \right) \ne 0$ is odd, and that if this coefficient is negative, the periodic orbits obtained in Theorem 3.1 by use of the implicit function theorem are attracting and occur for µ < 0 (we assume we have enough differentiability so that V is Cⁿ).